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In DeltaABC, with usual notations, if a,...

In `DeltaABC`, with usual notations, if a,b,c are in AP then `acos^(2)((C)/(2))+cos^(2)((A)/(2))=`

A

`(3a)/(2)`

B

`(3c)/(2)`

C

`(3b)/(2)`

D

`(3abc)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given a, b, c are in AP
`:.2b=a+c`
Now, `a cos^(2). (C)/(2) + c cos^(2). (A)/(2)`
`rArr a((1+cos C)/(2))+c((1+cos A)/(2)) [ :. 2 cos^(2) . (x)/(2) = 1+ cos x]`
`=(1)/(2)[ a+c+a cos C + c cos A]`
`=(1)/(2) [ 2b+b]= (3b)/(2) [ :' b=a cos C + c cos A]`
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